Integrator for circular ordinates



Dec. 2, 1941. w. H. KLIEVER 2,264,910v INTEGRATOR FOR CIRCULAR ORDINATESFiled "March 1, 1941 WALDo H. KLIEYER, uvwvrox By 2 ATTORNEYS PatentedDec. 2, 1941 QFFICE INTEGRATOR FOR CIRCULAR ORDINATES Waldo H. Kliever,Minneapolis, Minn; dedicated to. the free use of the People in theterritory of the United States Application March 1, 1941, Serial No;381,275

(Granted under the act of March 3, 1883, as amended April 30, 1928; 370G. 757) 3 Claims.

This application is made under the act of March 3, 1883, as amended bythe act of April 30, 1928, and the invention herein described andclaimed, if patented, may be manufactured and used by or for theGovernment of the United States of America for governmental purposeswithout the payment to me of any royalty thereon.

I hereby dedicate the invention herein described to the free use of thePeople in the territory of the United States to take effect on thegranting of a patent to me.

This invention rel-ates to integrators, and comprises an integrator foruse on charts obtained with recording instruments which use a continuousruled band of paper upon which the pen or pencil of the recordinginstrument swings in an arc in recording data. These charts are general-1y referred to as circular ordinate charts.

The curve obtained by this method of recording renders it extremelydifficult to calculate the time integral of the quantity measured, sincethis integral is not equal to the area below the curve, and the ordinaryuse of a planimeter or other conventional integrator cannot be made.

An object of this invention is the provision of an instrument which canbe used to integrate circular ordinate charts.

Another object of this invention is the provision of such an instrumentwhich is simple to construct and which is convenient and rapid to use.

The following description, considered together with the accompanyingdrawing, will disclose this invention more fully, and further objectsand advantages thereof will be apparent.

In the drawing:

Figure 1 is a plan view partly in section of a preferred embodiment ofthis invention, illustrating the method of using it; and

Figure 2 is a section on the line 22 of Figure 1.

Referring with more particularity to the drawing, in which like numeralsdesignate like parts, the embodiment illustrated comprises a guide rodit], which is adapted to be placed over a plane surf-ace H, such as thetop of a table, along one edge thereof, substantially as shown. Acarriage I2 is provided with grooved rollers I3 and I4 which travel onthe guide rod Ill. A trunnion roller I5 is mounted on the carriage l2 tosupport said carriage on the plane surface ll, thereby permitting thecarriage to be moved along the guide rod it with ease. A rod i6 ismounted on the carriage l2 and is slidable thereover in a directionperpendicular to the guide rod l0 and is disposed through aperture 9 anda bracket 8 fixed to the carriage l2. Adjacent to rod Hi there isrotatably mounted a drum I'I. Generally, the drum I! will be circular,but other shapes may be used for special cases. The drum l1 and the rodI6 are operatively connected by any suitable means. The meansillustrated comprise a pair of flexible bands l8 and I9, one end of eachof which is secured to the drum I! at 20 and 2|, respectively; The otherends, 22 and 23, respectively, of said bands extend tangentially fromsaid drum, being secured to the rod H3 substantially as illustrated.Other means of operatively connecting the drum 1! and the rod It may beemployed, such as rack and pinion means, but the means illustrated ispreferred since it produces a smooth tangent motion without backlash.

. There is radially secured to the drum I! a tracing arm 24 having acommon pivot with said drum IT at one end, the other end carrying atracer 25. The tracer 25 may be of any suitable design, but the typeillustrated is preferred and comprises a transparent plate 26 supportedon the bottom of a ring 21. The plate 26 is provided with a referencemark 30, which may be etched, embossed, or otherwise. inscribed, and ispreferably a small circle, so that in tracing a curve the operator,looking directly through the transparent plate 26, simply maintains thecurve diametrically through the circuit. This type of tracer providesfull visibility and makes it easy for the operator to trace a curve. Thedistance between the axis of the drum I1 and the center of the mark 30must be equal to the radius of curvature of the circular ordinates ofthe chart to be integrated. The polar arm 28 of a planimeter 29 is fixedon the'carriage l2 parallel to the rod It by means of a smallindentation (not shown) in the carriage I2 to receive the pivot point 3|of the polar arm, and adjustable abutment screws 32 and 33, carried bybrackets 34 and 35, respectively, laterally straddling said polar arm.The tracing arm 36 of the planimeter is attached to the rod it. Thisattachment may be accomplished by securing a lug 31 on the rod IS with agroove 38 parallel to the guide rod l0 and placing the tracing point 39of the arm 36 in the groove 38. However, any other suitable arrangementmay be used for the purpose. If desired, the polar arm 28 may be omittedentirely by pivoting one end of the arm 36 to the carriage 12. This is,in efiect, what is accomplished by fixing the polar arm as illustrated,since the polar arm in this position simply becomes an extension of thecarriage 12 with vertical freedom of motion. The integrating wheel 40carried by the arm 36 is disposed so as to contact the plane surface H.The illustrated method of mounting the polar arm 28 is preferred sinceit insures the fact that the integrating wheel 40 will rest on the tablesurface with uniform pressure under the weight of the planimeter.

To use this device the chart 4| to be integrated is placed on the planesurface II and the guide rod l0 clamped thereon parallel to the timeaxis of the chart and such that the tracing arm 24 occupies the samerelative position with respect to the chart that was occupied by therecording arm of the recording instrument, and so that when the tracerfollows the o-abscissa, no reading is accumulated on the integratingwheel of the planimeter. The tracer 25 is then placed on the curve 32 atthe initial position and the reading of the integrating wheel 40 isrecorded. The curve 42 is then traced out with the tracer 25, duringwhich the carriage [2 moves along the time axis with the tracer. to restat the end of each measurement on the same abscissa of the chart onwhich the measurement was begun. The o-abscissa will generally beselected for this purpose. At the completion of the tracing operationthe integrating wheel is again read. From this reading the recordedinitial reading is subtracted, the difference being proportional to thearea under the curve.

The principle of operation of this invention is as follows: The usualtype of integrator records the area under the curve of a chart as jydxwhere y is the distance straight across the chart and x is distancealong the time axis. The problem solved by the present invention is thatof providing an instrument with an integrating wheel which converts theangle A which the pen arm of the recording instrument makes with itszero position into y, or into the sin B where B is the angle which theaxis of the integrating wheel makes with its zero position, that is, theposition where the integrating wheel will not rotate when the carriageis moved along the time axis.

If the tracer arm 24 has an effective length 10 equal to the pen arm ofthe recording instrument upon Which the integrated curve was made, and

the pivot point of the tracing arm 24 moves along the chart parallel tothe time axis in the same relative position as the pen arm of therecording instrument, then, if the zero position of the chart is takento correspond to the position of zero angle of the tracer arm, theangular position of the tracing arm for any point on the curve will bethe same as that originally assumed by the recording pen arm at thatpoint, which is generally proportional to the quantity being measured,such as watts. Assuming that the wheel IT has a radius r, and that theeifective length of The tracer must come Since 1/ equals TA, where A ismeasured in radians, therefore,

sin B== sin B= Since the reading of the integrating wheel isproportional to the sin B and to distance along the time axis, it is,therefore, from Equation 2 also proportional to A. Therefore, theintegrating wheel gives fsin Bdat, which is proportional to Mali". 1*,i, and p, being constant, they can be varied to give any proportion ofthe integral quantity.

Having thus described my invention, I claim:

1. An integrator comprising a carriage movable over a plane surface,means for guiding said carriage in a straight line, a rod slidablymounted on said carriage, said rod being slidable on said carriage inthe direction perpendiculan to the movement of said carriage, meansincluding a drum rotatably mounted on said carriage to slidably actuatesaid rod, tracing means radially secured to said drum, an arm having oneend pivoted to said carriage and the other end comovable with said rod,and an integrating wheel on said arm, said integrating wheel beingdisposed so as to contact the plane surface.

2. An integrator comprising a carriage movable over a plane surface,means for guiding said carriage in a straight line, a rod slidablymounted on said carriage, said rod being slidable on said carriage inthe direction perpendicular to the movement of said carriage, meansincluding a drum rotatably mounted on said carriage to slidably actuatesaid rod, tracing means radially secured to said drum, and a polarplanimeter having its polar arm secured to said carriage and having theend of its tracing arm comovable with said rod, the integrating wheel ofsaid planimeter being disposed so as to contact the plane surface.

3. An integrator comprising a carriage movable over a plane surface,means for guiding said carriage in a straight line, a rod slidablymounted on said carriage, said rod being slidable on said carriage inthe direction perpendicular to the movement of said carriage, a drumrotatably ounted on said carriage, a pair of flexible links disposedabout the periphery of said drum in opposite directions, one end of eachof said links being secured to said drum, the other ends of said linksextending tangentially over said drum and being secured to said rod,tracing means radially secured to said drum, an arm having one endpivoted to said carriage and having its other end comovable with saidrod, and an integrating Wheel on said arm disposed so as to contact theplane surface.

WALDO H. KLIEVER.

